Some identities involving multiplicative semiderivations on ideals
Yıl: 2021 Cilt: 50 Sayı: 4 Sayfa Aralığı: 963 - 969 Metin Dili: İngilizce DOI: 10.15672/hujms.650600 İndeks Tarihi: 29-07-2022
Some identities involving multiplicative semiderivations on ideals
Öz: Let $R$ be a prime ring and $I$ be a nonzero ideal of $R.$ A mapping $d:Rrightarrow R$ is called a multiplicative semiderivation if there exists a function $g:Rrightarrow R$ such that (i) $d(xy)=d(x)g(y)+xd(y)=d(x)y+g(x)d(y)$ and (ii) $d(g(x))=g(d(x))$ hold for all $x,yin R.$ In the present paper, we shall prove that $[x,d(x)]=0,$ for all $xin I$ if any of the followings holds: i) $d(xy)pm xyin Z,$ ii) $d(xy)pm yxin Z,$ iii) $d(x)d(y)pm xyin Z,$ iv) $d(xy)pm d(x)d(y)in Z,$ viii) $d(xy)pm d(y)d(x)in Z,$ for all $x,yin I.$ Also, we show that $R$ must be commutative if $d(I)subseteq Z.$
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] O. Ağırtıcı and Ö. Gölbaşı, Multiplicative semiderivations on ideals of semiprime rings, Palest. J. Math. 9 (2), 792-800, 2020.
- [2] M. Ashraf and N. Rehman, On derivations and commutativity in prime rings, East- West J. Math. 3 (1), 87–91, 2001.
- [3] H.E. Bell and L.C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar. 53, 339-346, 1989.
- [4] J. Bergen, Derivations in prime rings, Canad. Math. Bull. 26, 267-270, 1983.
- [5] M. Bresar, Centralizing mappings and derivations in prime rings, J. Algebra 156, 385-394, 1983.
- [6] J.C. Chang, On semiderivations of prime rings, Chinese J. Math. 12, 255-262, 1984.
- [7] M.N. Daif, When is a multiplicative derivation additive, Int. J. Math. Math. Sci. 14 (3), 615-618, 1991.
- [8] B. Dhara and S. Ali, On multiplicative (generalized) derivation in prime and semiprime rings, Aequationes Math. 86, 65-79, 2013.
- [9] H. Goldman and P. Semrl, Multiplicative derivations on C(X), Monatsh Math. 121 (3), 189-197, 1969.
- [10] W.S. Martindale III, When are multiplicative maps additive, Proc. Amer. Math. Soc. 21, 695-698, 1969.
- [11] E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8, 1093-1100, 1957.
| APA | Gölbaşı Ö, bedir z (2021). Some identities involving multiplicative semiderivations on ideals. , 963 - 969. 10.15672/hujms.650600 |
| Chicago | Gölbaşı Öznur,bedir zeliha Some identities involving multiplicative semiderivations on ideals. (2021): 963 - 969. 10.15672/hujms.650600 |
| MLA | Gölbaşı Öznur,bedir zeliha Some identities involving multiplicative semiderivations on ideals. , 2021, ss.963 - 969. 10.15672/hujms.650600 |
| AMA | Gölbaşı Ö,bedir z Some identities involving multiplicative semiderivations on ideals. . 2021; 963 - 969. 10.15672/hujms.650600 |
| Vancouver | Gölbaşı Ö,bedir z Some identities involving multiplicative semiderivations on ideals. . 2021; 963 - 969. 10.15672/hujms.650600 |
| IEEE | Gölbaşı Ö,bedir z "Some identities involving multiplicative semiderivations on ideals." , ss.963 - 969, 2021. 10.15672/hujms.650600 |
| ISNAD | Gölbaşı, Öznur - bedir, zeliha. "Some identities involving multiplicative semiderivations on ideals". (2021), 963-969. https://doi.org/10.15672/hujms.650600 |
| APA | Gölbaşı Ö, bedir z (2021). Some identities involving multiplicative semiderivations on ideals. Hacettepe Journal of Mathematics and Statistics, 50(4), 963 - 969. 10.15672/hujms.650600 |
| Chicago | Gölbaşı Öznur,bedir zeliha Some identities involving multiplicative semiderivations on ideals. Hacettepe Journal of Mathematics and Statistics 50, no.4 (2021): 963 - 969. 10.15672/hujms.650600 |
| MLA | Gölbaşı Öznur,bedir zeliha Some identities involving multiplicative semiderivations on ideals. Hacettepe Journal of Mathematics and Statistics, vol.50, no.4, 2021, ss.963 - 969. 10.15672/hujms.650600 |
| AMA | Gölbaşı Ö,bedir z Some identities involving multiplicative semiderivations on ideals. Hacettepe Journal of Mathematics and Statistics. 2021; 50(4): 963 - 969. 10.15672/hujms.650600 |
| Vancouver | Gölbaşı Ö,bedir z Some identities involving multiplicative semiderivations on ideals. Hacettepe Journal of Mathematics and Statistics. 2021; 50(4): 963 - 969. 10.15672/hujms.650600 |
| IEEE | Gölbaşı Ö,bedir z "Some identities involving multiplicative semiderivations on ideals." Hacettepe Journal of Mathematics and Statistics, 50, ss.963 - 969, 2021. 10.15672/hujms.650600 |
| ISNAD | Gölbaşı, Öznur - bedir, zeliha. "Some identities involving multiplicative semiderivations on ideals". Hacettepe Journal of Mathematics and Statistics 50/4 (2021), 963-969. https://doi.org/10.15672/hujms.650600 |
